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Transactions of the American Mathematical Society

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Spectral properties of tensor products of linear operators. II. The approximate point spectrum and Kato essential spectrum


Author: Takashi Ichinose
Journal: Trans. Amer. Math. Soc. 237 (1978), 223-254
MSC: Primary 47A10
DOI: https://doi.org/10.1090/S0002-9947-1978-0479372-0
MathSciNet review: 479372
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Abstract: For tensor products of linear operators, their approximate point spectrum, approximate deficiency spectrum and essential spectra in the sense of T. Kato and Gustafson-Weidmann are determined together with explicit formulae for their nullity and deficiency. The theory applies to $ A \otimes I + I \otimes B$ and $ A \otimes B$.


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DOI: https://doi.org/10.1090/S0002-9947-1978-0479372-0
Keywords: Topological tensor products, operators on tensor products of Banach spaces, separation of variables, spectral mapping theorem, spectrum, approximate point spectrum, essential spectrum, semi-Fredholm operator, nullity and deficiency of operators
Article copyright: © Copyright 1978 American Mathematical Society